You're welcome.
I don't think either of those will cut it long enough for even a single (complete) recharge. They play with numbers, of course just to make it more fun. Like quoting a built in battery of XX capacity without telling you that's at 3.6 Volts average. Which has to be multiplied (from our POV) up to 5.0 or worse still, 12 Volts to be used. From the poor batteries POV it's a division of course. And we to 'cover' losses due to heat and such in the process. We only get maybe 1/4 of the capacity claimed to charge our Solo in the end. If it's honest, sad to say that's often not the case. For instance, I'm not sure I believe the 20,000mAh claim, at least until I learn more about the magic involved...... Solo II is state of the art here, at 1/6 of that?
I still think the best way to go is with the LED lighting guys. They are based on 12 Volts to start with, and are basically (Protected) batteries in a box. Nothing fancy. In an industry where you need to be at least somewhat honest as volume customers are sought on one side and dependability on the other. These from Amazon (or most of them anyway) should do fine, as are the same from EBay.
https://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias=aps&field-keywords=12+volt+battery+packs
The key is to start with 12 Volts? Converting up is a bad call if you want 'bang for the buck'. Charging Solo is a whole lot like powering LED lighting at a party? If you're the battery. Both are from the fun food group.....
The cable might or might not work on the Solo end (some do, some don't). Sometimes you need to trim a 'doughnut' off the plastic part like this:
I don't have that cable, so can't confirm things. I have given a couple I've used. I've only met one that couldn't be 'cut back' enough to work.
However, no way will it work with a battery pack made to work with USBs. Think about it, if the battery pack put 12 Volts not 5 into your cell phone...... OK for Air, probably.
Yes, as you've noted, Arizer is 'cheating' a bit on the connector (running more voltage than spec) so 'nobody' uses that connector at 12 Volts. Accept the 5.5mm one, it is the standard in a couple of related industries. Adapters are your friend often.
The general answer you asked for is 'yes, you can recharge Solo II from a battery pack', but you have to be a bit careful doing so or you end up with a
few, slow recharges. Perhaps not even a single complete one?
OF